Cut about an inch off the top and bottom of the Poblano and remove the seeds, leaving body intact. Place the chiles in the freezer for at least 1 hour and up to 24 hours.
In a mixing glass, muddle the cilantro, add the rest of the ingredients, add ice and shake 12 to 14 times. Place the frozen poblano in a pint glass and pour the drink over it. (Alternatively, this cocktail can be served in a martini glass.)